[math]\pi = 4 \sum_{n=0}^{\infty} \frac{(-1)^n}{2n+1}[/math]
I calculated the integer sum steps required to complete each numerical place, note that these numbers are fundamental to this equation and are independent of any computer specifications. (i.e. CPU, RAM, Memory, OS, basic language, etc.)
Integer sum:
[math]n \; ( \text{2}, \text{18}, \text{118}, \text{1687}, \text{10793}, \text{136120}, \text{1530011}, \text{18660287}, \text{155974698})[/math]
Numerical place:
[math]n_l \; (3,1,4,1,5,9,2,6,5)[/math]
Numerical length:
[math]l \; (1,2,3,4,5,6,7,8,9)[/math]
Example:
[math]4 \sum_{n=0}^{1687} \frac{(-1)^n}{2n+1} = 3.141... \; \; \; l = 4[/math]
Note that [math]l = 9[/math] required a compiler.